Exact analytic solutions of the lubrication equations for squeeze-flow of a biviscous fluid between two parallel disks

Based on lubrication approximation, the squeezing flow of biviscous fluids between two parallel disks with partial slip boundary condition was investigated. In addition to the solution of the kinematics in the bi-viscosity region leading to a cubic equation of the yield surface, the full explicit expressions of radial pressure gradient, pressure and squeeze force are given in the exact relationships. According to three dimensionless numbers, different behaviors are covered including Bingham fluid as a limiting case of bi-viscosity model. Besides, a critical force separating the Newtonian and biviscous regions of the flow is provided. However, for a flow of a Bingham fluid without wall slip, the expression of the applied force may be expressed or not according to the yield stress. This depends on the ratio value of the characteristic time of the fluid to the time scale of observation if it is very lower or higher than unity.

► Exact solution of the squeeze force for a biviscous fluid is obtained.
► Bingham fluid is presented as a limiting case of bi-viscosity model.
► Relationships of the force are given according to slip coefficient and yield number.
► The squeeze force for a Bingham fluid should be larger than a threshold force.
► Below this force the fluid is Newtonian and this is linked to a dimensionless number.